Math Help - Tricky Transposition of Formula

1. Tricky Transposition of Formula

Hi there, I am studying for an engineering degree, and need to transpose this formula. I'm normally ok at this, however on this particular one I keep getting a very slightly different answer to the text book.

I need to transpose this for (A2):

q=(A)squareroot[(2gh/(A/A2)^2 -1]

Sorry about the messy presentation, I don't know how to use the code to make nice formulas! The bit in [square brackets] is all uner the squareroot.

A2=+/- squareroot[(q^2)(A^2)-q^2/2ghA2]

In the text book, the -q^2 is +q^2 and is on the bottom of the fraction.

Any help with this would be greatly appriciated.

2. Originally Posted by mikewhant
I need to transpose this for (A2):

q=(A)squareroot[(2gh/(A/A2)^2 -1]

$q = A\sqrt{\frac{2gh}{\left(\frac{A}{A_2}\right)^2 - 1}}$

or

$q = A\sqrt{\frac{2gh}{\left(\frac{A}{A_2}\right)^2} - 1}$

what you posted is the second interpretation.

3. Hello,

It is the first one you posted. Sorry about that!

Thanks, Mike

4. $q = A\sqrt{\frac{2gh}{\left(\frac{A}{A_2}\right)^2 - 1}}$

$\frac{q}{A} = \sqrt{\frac{2gh}{\left(\frac{A}{A_2}\right)^2 - 1}}$

$\frac{q^2}{A^2} = \frac{2gh}{\frac{A^2}{A_2^2} - 1}$

$\frac{q^2}{A^2} = \frac{2A_2^2gh}{A^2 - A_2^2}$

$q^2(A^2 - A_2^2) = 2A^2A_2^2gh$

$q^2A^2 = 2A^2A_2^2gh + q^2A_2^2$

$q^2A^2 = A_2^2(2A^2gh + q^2)$

$\frac{q^2A^2}{2A^2gh + q^2} = A_2^2$

$\pm \sqrt{\frac{q^2A^2}{2A^2gh + q^2}} = A_2$

what a mess ...

5. Thanks alot, I was going wrong on the 4th line.

Take care and thanks again!

Mike